Abstract and concrete categories
Abstract and concrete categories
Pushout-complements and basic concepts of grammars in toposes
Theoretical Computer Science
Introduction to the Algebraic Theory of Graph Grammars (A Survey)
Proceedings of the International Workshop on Graph-Grammars and Their Application to Computer Science and Biology
Algebraic Approach to Graph Transformation Based on Single Pushout Derivations
WG '90 Proceedings of the 16rd International Workshop on Graph-Theoretic Concepts in Computer Science
Fundamentals of Algebraic Graph Transformation (Monographs in Theoretical Computer Science. An EATCS Series)
Graph-grammars: An algebraic approach
SWAT '73 Proceedings of the 14th Annual Symposium on Switching and Automata Theory (swat 1973)
ICGT'06 Proceedings of the Third international conference on Graph Transformations
A framework for families of domain-specific modelling languages
Software and Systems Modeling (SoSyM)
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In category theory, most set-theoretic constructions-union, intersection, etc.-have direct categorical counterparts. But up to now, there is no direct construction of a deletion operation like the set-theoretic complement. In rule-based transformation systems, deletion of parts of a given object is one of the main tasks. In the double pushout approach to algebraic graph transformation, the construction of pushout complements is used in order to locally delete structures from graphs. But in general categories, even if they have pushouts, pushout complements do not necessarily exist or are unique. In this paper, two different constructions for pushout complements are given and compared. Both constructions are based on certain universal constructions in the sense of category theory. More specifically, one uses initial pushouts while the other one uses quasi-coproduct complements. These constructions are applied to examples in the categories of graphs and simple graphs.